All prime squares have exactly three factors.
49 has exactly three factors: 1, 7, and 49.
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A number has exactly three factors if and only if it is the square of a prime number.
There are an infinite number of them. 8 has three prime factors, 30 is the first with three distinct prime factors.
30
625
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.